Finite Group Databasebeta

← C31×#23894 #21480653

Subgroups — C31×#23894 #21480653

Order 7936.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3586C211yesmaximal, characteristic, complemented
2C31×#3585C211yesmaximal, characteristic, complemented
3C31×#3020C211yesmaximal, characteristic, complemented
4C31×#3019C211yesmaximal, characteristic, complemented
5C31×#3010C211yesmaximal, characteristic, complemented
6C31×#3009C211yesmaximal, characteristic, complemented
7C31×#2019C211yesmaximal, characteristic, complemented
8C31×#2017C211yesmaximal, characteristic, complemented
9C31×#2009C211yesmaximal, characteristic, complemented
10C31×#2008C211yesmaximal, characteristic, complemented
11C31×#1903C211yesmaximal, characteristic, complemented
12C31×#1902C211yesmaximal, characteristic, complemented
13C31×#1881C211yesmaximal, characteristic, complemented
14C31×#1881C211yesmaximal, characteristic, complemented
15C31×#1794C211yesmaximal, characteristic, complemented
16C31×#585C2211yescharacteristic
17C2×C31×2−1+4C2211yescharacteristic, complemented
18C2×C31×H(5,𝔽2)C2211yescharacteristic
19C31×#578—22no—
20C31×#578—22no—
21C31×#577—22no—
22C31×#577—22no—
23C31×#577—22no—
24C31×#577—22no—
25C31×#576—22no—
26C31×#576—22no—
27C31×#575—22no—
28C31×#575—22no—
29C31×#575C2211yescharacteristic
30C31×#575C2211yescharacteristic
31C31×#575C2211yescharacteristic
32C31×#575C2211yescharacteristic, complemented
33C31×#575C2211yescharacteristic, complemented
34C2×C31×#137—22no—
35C2×C31×#137C2211yescharacteristic
36C2×C31×#137C2211yescharacteristic, complemented
37C2×C31×AGL(1,ℤ/8)—22no—
38C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
39C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
40C22×SD16×C31C2211yescharacteristic, complemented
41C31×#568C2211yescharacteristic
42C31×#568C2211yescharacteristic, complemented
43C31×#536C2211yescharacteristic, complemented
44C31×#535C2211yescharacteristic, complemented
45C31×#456—22no—
46C31×#455—22no—
47C31×#454—22no—
48C31×#453—22no—
49C31×#452—22no—
50C31×#450—22no—
51C31×#449—22no—
52C31×#448—22no—
53C31×#421C2211yescharacteristic
54C31×#421C2211yescharacteristic, complemented
55C31×#421C2211yescharacteristic, complemented
56C31×#421C2211yescharacteristic, complemented
57C31×#419C2211yescharacteristic, complemented
58C31×#418C2211yescharacteristic, complemented
59C31×#416C2211yescharacteristic
60C31×#416C2211yescharacteristic, complemented
61C2×C31×#101C2211yescharacteristic, complemented
62C2×C31×#100C2211yescharacteristic, complemented
63C31×#410C2211yescharacteristic, complemented
64C31×#408C2211yescharacteristic, complemented
65C31×#408C2211yescharacteristic, complemented
66C31×#408C2211yescharacteristic, complemented
67C31×#344C2211yescharacteristic, complemented
68C31×#344C2211yescharacteristic, complemented
69C31×#341C2211yescharacteristic, complemented
70C31×#338C2211yescharacteristic, complemented
71C31×2−1+4—22no—
72C31×2−1+4—21no—
73C31×2−1+4—22no—
74C31×2−1+4—21no—
75C31×2−1+4—22no—
76C31×2−1+4—41no—
77C31×2−1+4D412yescomplemented
78C31×H(5,𝔽2)—22no—
79C31×H(5,𝔽2)—21no—
80C31×H(5,𝔽2)—22no—
81C31×H(5,𝔽2)—21no—
82C31×H(5,𝔽2)—22no—
83C31×H(5,𝔽2)—41no—
84C31×H(5,𝔽2)—41no—
85C31×H(5,𝔽2)D412yescomplemented
86C2×#41×C31—22no—
87C2×#41×C31—22no—
88C2×#41×C31—21no—
89C2×#41×C31—21no—
90C2×#41×C31—21no—
91C2×#41×C31—21no—
92C2×#41×C31—41no—
93C2×#41×C31—41no—
94C2×#41×C31C2311yescharacteristic
95C2×#41×C31C2311yescharacteristic
96C2×#41×C31C2311yescharacteristic
97C2×#41×C31C2311yescharacteristic
98C2×#41×C31C2311yescharacteristic
99C22×Q8×C31—21no—
100C22×Q8×C31—21no—
101C22×Q8×C31C2311yescharacteristic
102C22×D4×C31—21no—
103C22×D4×C31—21no—
104C22×D4×C31—41no—
105C22×D4×C31C2311yescharacteristic
106C31×#137—24no—
107C31×#137—24no—
108C31×#137—24no—
109C31×#137—24no—
110C31×#137—22no—
111C31×#137—22no—
112C31×#137—21no—
113C31×#137—22no—
114C31×#137—21no—
115C31×#137—21no—
116C31×#137—21no—
117C31×#137—21no—
118C31×#137—21no—
119C31×#137—21no—
120C31×#137—21no—
121C31×#137—22no—
122C31×#137D412yes—
123C31×#137D412yescomplemented
124C31×AGL(1,ℤ/8)—24no—
125C31×AGL(1,ℤ/8)—24no—
126C31×AGL(1,ℤ/8)—24no—
127C31×AGL(1,ℤ/8)—24no—
128C31×AGL(1,ℤ/8)—22no—
129C31×AGL(1,ℤ/8)—22no—
130C31×AGL(1,ℤ/8)—21no—
131C31×AGL(1,ℤ/8)—22no—
132C31×AGL(1,ℤ/8)—21no—
133C31×AGL(1,ℤ/8)—21no—
134C31×AGL(1,ℤ/8)—21no—
135C31×AGL(1,ℤ/8)—21no—
136C31×AGL(1,ℤ/8)—21no—
137C31×AGL(1,ℤ/8)—21no—
138C31×AGL(1,ℤ/8)—21no—
139C31×AGL(1,ℤ/8)—22no—
140C31×AGL(1,ℤ/8)D412yes—
141C31×AGL(1,ℤ/8)D412yescomplemented
142C31×#135—24no—
143C31×#135—24no—
144C31×#135—24no—
145C31×#135—24no—
146C31×#135—22no—
147C31×#135—22no—
148C31×#135—22no—
149C31×#135—22no—
150C31×#135—41no—
151C2×Q16×C31—24no—
152C2×Q16×C31—21no—
153C2×Q16×C31D412yescomplemented
154C2×SD16×C31—24no—
155C2×SD16×C31—24no—
156C2×SD16×C31—21no—
157C2×SD16×C31—21no—
158C2×SD16×C31—22no—
159C2×SD16×C31—22no—
160C2×SD16×C31—41no—
161C2×SD16×C31D412yes—
162C2×SD16×C31D412yescomplemented
163C2×D8×C31—24no—
164C2×D8×C31—21no—
165C2×D8×C31D412yes—
166C31×#131—22no—
167C31×#131—22no—
168C31×#131—22no—
169C31×#131—22no—
170C2×M16×C31—22no—
171C2×M16×C31—22no—
172C2×M16×C31C2311yescharacteristic
173C2×M16×C31C2311yescharacteristic
174C2×M16×C31C2311yescharacteristic
175C2×M16×C31C2311yescharacteristic
176C2×M16×C31C2311yescharacteristic
177C22×C8×C31C2311yescharacteristic
178C31×C4⋊Q8—21no—
179C31×#127—21no—
180C31×#124—21no—
181C31×#124—21no—
182C31×#123—41no—
183C31×C22⋊Q8—22no—
184C31×#121—22no—
185C31×#120—41no—
186C31×#117C2311yescharacteristic
187C31×#117C2311yescharacteristic
188C31×#104—22no—
189C31×#104—22no—
190C31×#104—22no—
191C31×#104—22no—
192C31×#103—21no—
193C31×#103—21no—
194C31×#103—22no—
195C31×#102—21no—
196C31×#102—21no—
197C31×#102—22no—
198C31×#101—22no—
199C31×#100—22no—
200C31×#99—41no—
201C31×C22⋊C8—22no—
202C31×C22⋊C8—22no—
203C31×C22⋊C8—41no—
204C24×C31—21no—
205C24×C31—41no—
206#41×C31—21no—
207#41×C31—21no—
208#41×C31—21no—
209#41×C31—21no—
210#41×C31—24no—
211#41×C31—24no—
212#41×C31—22no—
213#41×C31—22no—
214#41×C31—22no—
215#41×C31—22no—
216#41×C31—21no—
217#41×C31—21no—
218#41×C31—21no—
219#41×C31—21no—
220#41×C31—21no—
221#41×C31—21no—
222#41×C31—21no—
223#41×C31—21no—
224#41×C31—21no—
225#41×C31—21no—
226#41×C31—21no—
227#41×C31—21no—
228#41×C31—42no—
229#41×C31—42no—
230#41×C31—42no—
231#41×C31—42no—
232#41×C31—42no—
233#41×C31—44no—
234#41×C31—42no—
235#41×C31—42no—
236#41×C31—42no—
237#41×C31—41no—
238#41×C31—41no—
239#41×C31—44no—
240#41×C31—42no—
241#41×C31—42no—
242#41×C31C2×D412yes—
243#41×C31C2×D412yes—
244#41×C31C2×D412yes—
245#41×C31C2×D412yes—
246C2×Q8×C31—21no—
247C2×Q8×C31—24no—
248C2×Q8×C31—22no—
249C2×Q8×C31—22no—
250C2×Q8×C31—21no—
251C2×Q8×C31—21no—
252C2×Q8×C31—21no—
253C2×Q8×C31—21no—
254C2×Q8×C31—41no—
255C2×Q8×C31—42no—
256C2×Q8×C31—42no—
257C2×Q8×C31—41no—
258C2×Q8×C31—42no—
259C2×Q8×C31C2×D412yes—
260C2×Q8×C31C2×D411yescharacteristic
261C2×Q8×C31C2×D411yescharacteristic
262C2×Q8×C31C2×D411yescharacteristic
263C2×Q8×C31C2×D411yescharacteristic
264C2×Q8×C31C2×D411yescharacteristic
265C2×D4×C31—21no—
266C2×D4×C31—21no—
267C2×D4×C31—24no—
268C2×D4×C31—22no—
269C2×D4×C31—22no—
270C2×D4×C31—21no—
271C2×D4×C31—21no—
272C2×D4×C31—21no—
273C2×D4×C31—21no—
274C2×D4×C31—21no—
275C2×D4×C31—21no—
276C2×D4×C31—21no—
277C2×D4×C31—21no—
278C2×D4×C31—42no—
279C2×D4×C31—41no—
280C2×D4×C31—41no—
281C2×D4×C31—42no—
282C2×D4×C31—42no—
283C2×D4×C31—41no—
284C2×D4×C31—44no—
285C2×D4×C31—42no—
286C2×D4×C31—42no—
287C2×D4×C31—44no—
288C2×D4×C31—41no—
289C2×D4×C31—42no—
290C2×D4×C31—42no—
291C2×D4×C31C2×D412yes—
292C2×D4×C31C2×D411yescharacteristic
293C2×D4×C31C2×D411yescharacteristic
294C2×D4×C31C2×D411yescharacteristic
295C2×D4×C31C2×D411yescharacteristic
296C2×D4×C31C2×D411yescharacteristic
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—41no—
304C22×C4×C31—42no—
305C22×C4×C31—41no—
306C22×C4×C31—41no—
307C22×C4×C31C2411yescharacteristic
308Q16×C31—24no—
309Q16×C31—22no—
310Q16×C31—22no—
311Q16×C31—22no—
312Q16×C31—24no—
313Q16×C31—22no—
314Q16×C31—41no—
315SD16×C31—24no—
316SD16×C31—22no—
317SD16×C31—24no—
318SD16×C31—22no—
319SD16×C31—22no—
320SD16×C31—22no—
321SD16×C31—22no—
322SD16×C31—24no—
323SD16×C31—22no—
324SD16×C31—22no—
325SD16×C31—24no—
326SD16×C31—22no—
327SD16×C31—44no—
328SD16×C31—41no—
329SD16×C31—41no—
330D8×C31—24no—
331D8×C31—22no—
332D8×C31—22no—
333D8×C31—22no—
334D8×C31—24no—
335D8×C31—22no—
336D8×C31—41no—
337M16×C31—24no—
338M16×C31—24no—
339M16×C31—21no—
340M16×C31—21no—
341M16×C31—21no—
342M16×C31—21no—
343M16×C31—21no—
344M16×C31—21no—
345M16×C31—21no—
346M16×C31—21no—
347M16×C31C2×D412yes—
348M16×C31C2×D412yes—
349C2×C8×C31—24no—
350C2×C8×C31—24no—
351C2×C8×C31—21no—
352C2×C8×C31—21no—
353C2×C8×C31—21no—
354C2×C8×C31—21no—
355C2×C8×C31—21no—
356C2×C8×C31—21no—
357C2×C8×C31C2×D412yes—
358C2×C8×C31C2×D412yes—
359C4⋊C4×C31—21no—
360C4⋊C4×C31—21no—
361C4⋊C4×C31—42no—
362C22⋊C4×C31—21no—
363C22⋊C4×C31—21no—
364C22⋊C4×C31—42no—
365C22⋊C4×C31—42no—
366C42×C31—21no—
367C42×C31—21no—
368#23894C3111yesmaximal, characteristic, direct product factor, Sylow
369C23×C31—21no—
370C23×C31—21no—
371C23×C31—21no—
372C23×C31—21no—
373C23×C31—21no—
374C23×C31—22no—
375C23×C31—42no—
376C23×C31—44no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—161no—
380C23×C31—162no—
381C23×C31H(5,𝔽2)11yescharacteristic
382Q8×C31—21no—
383Q8×C31—21no—
384Q8×C31—21no—
385Q8×C31—21no—
386Q8×C31—22no—
387Q8×C31—21no—
388Q8×C31—21no—
389Q8×C31—22no—
390Q8×C31—21no—
391Q8×C31—21no—
392Q8×C31—42no—
393Q8×C31—44no—
394Q8×C31—41no—
395Q8×C31—41no—
396Q8×C31#12012yes—
397Q8×C31#12012yes—
398D4×C31—22no—
399D4×C31—22no—
400D4×C31—22no—
401D4×C31—22no—
402D4×C31—21no—
403D4×C31—21no—
404D4×C31—22no—
405D4×C31—21no—
406D4×C31—21no—
407D4×C31—21no—
408D4×C31—21no—
409D4×C31—21no—
410D4×C31—21no—
411D4×C31—22no—
412D4×C31—42no—
413D4×C31—42no—
414D4×C31—44no—
415D4×C31—42no—
416D4×C31—44no—
417D4×C31—44no—
418D4×C31—41no—
419D4×C31—41no—
420D4×C31—41no—
421D4×C31—41no—
422D4×C31—41no—
423D4×C31—41no—
424D4×C31—41no—
425D4×C31—41no—
426D4×C31—162no—
427D4×C31#12012yes—
428D4×C31#12012yes—
429C2×C4×C31—21no—
430C2×C4×C31—21no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—21no—
436C2×C4×C31—21no—
437C2×C4×C31—22no—
438C2×C4×C31—21no—
439C2×C4×C31—42no—
440C2×C4×C31—42no—
441C2×C4×C31—42no—
442C2×C4×C31—44no—
443C2×C4×C31—44no—
444C2×C4×C31—44no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31C22×D411yescharacteristic
456C2×C4×C31C22×D411yescharacteristic
457C2×C4×C31C22×D411yescharacteristic
458C2×C4×C31C22×D411yescharacteristic
459C2×C4×C31C22×D411yescharacteristic
460C2×C4×C31H(5,𝔽2)11yescharacteristic
461C8×C31—22no—
462C8×C31—22no—
463C8×C31—22no—
464C8×C31—22no—
465C8×C31—41no—
466C8×C31—41no—
467#3586C2×C3111yescharacteristic, complemented
468#3585C2×C3111yescharacteristic, complemented
469#3020C2×C3111yescharacteristic, complemented
470#3019C2×C3111yescharacteristic, complemented
471#3010C2×C3111yescharacteristic, complemented
472#3009C2×C3111yescharacteristic, complemented
473#2019C2×C3111yescharacteristic, complemented
474#2017C2×C3111yescharacteristic, complemented
475#2009C2×C3111yescharacteristic, complemented
476#2008C2×C3111yescharacteristic, complemented
477#1903C2×C3111yescharacteristic, complemented
478#1902C2×C3111yescharacteristic, complemented
479#1881C2×C3111yescharacteristic, complemented
480#1881C2×C3111yescharacteristic, complemented
481#1794C2×C3111yescharacteristic, complemented
482C22×C31—22no—
483C22×C31—22no—
484C22×C31—41no—
485C22×C31—42no—
486C22×C31—42no—
487C22×C31—41no—
488C22×C31—41no—
489C22×C31—41no—
490C22×C31—42no—
491C22×C31—81no—
492C22×C31—81no—
493C22×C31—82no—
494C22×C31—81no—
495C22×C31—82no—
496C22×C31—161no—
497C22×C31—162no—
498C22×C31—164no—
499C22×C31#53411yescharacteristic
500C22×C31D4211yescharacteristic
501C22×C31D4211yescharacteristic
502C4×C31—22no—
503C4×C31—22no—
504C4×C31—41no—
505C4×C31—41no—
506C4×C31—41no—
507C4×C31—42no—
508C4×C31—81no—
509C4×C31—81no—
510C4×C31C2×#12011yescharacteristic
511C4×C31C2×#12011yescharacteristic
512C4×C31D4211yescharacteristic
513C4×C31D4211yescharacteristic
514#585C22×C3111yescharacteristic
515C2×2−1+4C22×C3111yescharacteristic, complemented
516C2×H(5,𝔽2)C22×C3111yescharacteristic
517#578—22no—
518#578—22no—
519#577—22no—
520#577—22no—
521#577—22no—
522#577—22no—
523#576—22no—
524#576—22no—
525#575—22no—
526#575—22no—
527#575C22×C3111yescharacteristic
528#575C22×C3111yescharacteristic
529#575C22×C3111yescharacteristic
530#575C22×C3111yescharacteristic, complemented
531#575C22×C3111yescharacteristic, complemented
532C2×#137—22no—
533C2×#137C22×C3111yescharacteristic
534C2×#137C22×C3111yescharacteristic, complemented
535C2×AGL(1,ℤ/8)—22no—
536C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
537C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
538C22×SD16C22×C3111yescharacteristic, complemented
539#568C22×C3111yescharacteristic
540#568C22×C3111yescharacteristic, complemented
541#536C22×C3111yescharacteristic, complemented
542#535C22×C3111yescharacteristic, complemented
543#456—22no—
544#455—22no—
545#454—22no—
546#453—22no—
547#452—22no—
548#450—22no—
549#449—22no—
550#448—22no—
551#421C22×C3111yescharacteristic
552#421C22×C3111yescharacteristic, complemented
553#421C22×C3111yescharacteristic, complemented
554#421C22×C3111yescharacteristic, complemented
555#419C22×C3111yescharacteristic, complemented
556#418C22×C3111yescharacteristic, complemented
557#416C22×C3111yescharacteristic
558#416C22×C3111yescharacteristic, complemented
559C2×#101C22×C3111yescharacteristic, complemented
560C2×#100C22×C3111yescharacteristic, complemented
561#410C22×C3111yescharacteristic, complemented
562#408C22×C3111yescharacteristic, complemented
563#408C22×C3111yescharacteristic, complemented
564#408C22×C3111yescharacteristic, complemented
565#344C22×C3111yescharacteristic, complemented
566#344C22×C3111yescharacteristic, complemented
567#341C22×C3111yescharacteristic, complemented
568#338C22×C3111yescharacteristic, complemented
569C2×C31—21no—
570C2×C31—21no—
571C2×C31—21no—
572C2×C31—42no—
573C2×C31—42no—
574C2×C31—81no—
575C2×C31—81no—
576C2×C31—82no—
577C2×C31—81no—
578C2×C31#240311yescharacteristic
5792−1+4—22no—
5802−1+4—21no—
5812−1+4—22no—
5822−1+4—21no—
5832−1+4—22no—
5842−1+4—41no—
5852−1+4D4×C3112yescomplemented
586H(5,𝔽2)—22no—
587H(5,𝔽2)—21no—
588H(5,𝔽2)—22no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—22no—
591H(5,𝔽2)—41no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)D4×C3112yescomplemented
594C2×#41—22no—
595C2×#41—22no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—41no—
601C2×#41—41no—
602C2×#41C23×C3111yescharacteristic
603C2×#41C23×C3111yescharacteristic
604C2×#41C23×C3111yescharacteristic
605C2×#41C23×C3111yescharacteristic
606C2×#41C23×C3111yescharacteristic
607C22×Q8—21no—
608C22×Q8—21no—
609C22×Q8C23×C3111yescharacteristic
610C22×D4—21no—
611C22×D4—21no—
612C22×D4—41no—
613C22×D4C23×C3111yescharacteristic
614#137—24no—
615#137—24no—
616#137—24no—
617#137—24no—
618#137—22no—
619#137—22no—
620#137—21no—
621#137—22no—
622#137—21no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—22no—
630#137D4×C3112yes—
631#137D4×C3112yescomplemented
632AGL(1,ℤ/8)—24no—
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—22no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—21no—
639AGL(1,ℤ/8)—22no—
640AGL(1,ℤ/8)—21no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—22no—
648AGL(1,ℤ/8)D4×C3112yes—
649AGL(1,ℤ/8)D4×C3112yescomplemented
650#135—24no—
651#135—24no—
652#135—24no—
653#135—24no—
654#135—22no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—41no—
659C2×Q16—24no—
660C2×Q16—21no—
661C2×Q16D4×C3112yescomplemented
662C2×SD16—24no—
663C2×SD16—24no—
664C2×SD16—21no—
665C2×SD16—21no—
666C2×SD16—22no—
667C2×SD16—22no—
668C2×SD16—41no—
669C2×SD16D4×C3112yes—
670C2×SD16D4×C3112yescomplemented
671C2×D8—24no—
672C2×D8—21no—
673C2×D8D4×C3112yes—
674#131—22no—
675#131—22no—
676#131—22no—
677#131—22no—
678C2×M16—22no—
679C2×M16—22no—
680C2×M16C23×C3111yescharacteristic
681C2×M16C23×C3111yescharacteristic
682C2×M16C23×C3111yescharacteristic
683C2×M16C23×C3111yescharacteristic
684C2×M16C23×C3111yescharacteristic
685C22×C8C23×C3111yescharacteristic
686C4⋊Q8—21no—
687#127—21no—
688#124—21no—
689#124—21no—
690#123—41no—
691C22⋊Q8—22no—
692#121—22no—
693#120—41no—
694#117C23×C3111yescharacteristic
695#117C23×C3111yescharacteristic
696#104—22no—
697#104—22no—
698#104—22no—
699#104—22no—
700#103—21no—
701#103—21no—
702#103—22no—
703#102—21no—
704#102—21no—
705#102—22no—
706#101—22no—
707#100—22no—
708#99—41no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—41no—
712C31#2389411yescharacteristic, direct product factor, Sylow
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C3112yes—
752#41C2×D4×C3112yes—
753#41C2×D4×C3112yes—
754#41C2×D4×C3112yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C3112yes—
769C2×Q8C2×D4×C3111yescharacteristic
770C2×Q8C2×D4×C3111yescharacteristic
771C2×Q8C2×D4×C3111yescharacteristic
772C2×Q8C2×D4×C3111yescharacteristic
773C2×Q8C2×D4×C3111yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C3112yes—
801C2×D4C2×D4×C3111yescharacteristic
802C2×D4C2×D4×C3111yescharacteristic
803C2×D4C2×D4×C3111yescharacteristic
804C2×D4C2×D4×C3111yescharacteristic
805C2×D4C2×D4×C3111yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C3111yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C3112yes—
857M16C2×D4×C3112yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C3112yes—
867C2×C8C2×D4×C3112yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23C31×H(5,𝔽2)11yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8C31×#12012yes—
905Q8C31×#12012yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4C31×#12012yes—
936D4C31×#12012yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C3111yescharacteristic
964C2×C4C22×D4×C3111yescharacteristic
965C2×C4C22×D4×C3111yescharacteristic
966C2×C4C22×D4×C3111yescharacteristic
967C2×C4C22×D4×C3111yescharacteristic
968C2×C4C31×H(5,𝔽2)11yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C31×#53411yescharacteristic
993C22D42×C3111yescharacteristic
994C22D42×C3111yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×C31×#12011yescharacteristic
1004C4C2×C31×#12011yescharacteristic
1005C4D42×C3111yescharacteristic
1006C4D42×C3111yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C31×#240311yescharacteristic
subgroupG/H
center, socleC2×C31#2403
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C31×#3586C2semidirect
2. C31×#3585C2semidirect
3. C31×#3020C2semidirect
4. C31×#3019C2semidirect
5. C31×#3010C2semidirect
6. C31×#3009C2semidirect
7. C31×#2019C2semidirect
8. C31×#2017C2semidirect
9. C31×#2009C2semidirect
10. C31×#2008C2semidirect
11. C31×#1903C2semidirect
12. C31×#1902C2semidirect
13. C31×#1881C2semidirect
14. C31×#1881C2semidirect
15. C31×#1794C2semidirect
17. C2×C31×2−1+4C22semidirect
32. C31×#575C22semidirect
33. C31×#575C22semidirect
36. C2×C31×#137C22semidirect
40. C22×SD16×C31C22semidirect
42. C31×#568C22semidirect
43. C31×#536C22semidirect
44. C31×#535C22semidirect
54. C31×#421C22semidirect
55. C31×#421C22semidirect
56. C31×#421C22semidirect
57. C31×#419C22semidirect
58. C31×#418C22semidirect
60. C31×#416C22semidirect
61. C2×C31×#101C22semidirect
62. C2×C31×#100C22semidirect
63. C31×#410C22semidirect
64. C31×#408C22semidirect
65. C31×#408C22semidirect
66. C31×#408C22semidirect
67. C31×#344C22semidirect
68. C31×#344C22semidirect
69. C31×#341C22semidirect
70. C31×#338C22semidirect
77. C31×2−1+4D4semidirect
85. C31×H(5,𝔽2)D4semidirect
123. C31×#137D4semidirect
141. C31×AGL(1,ℤ/8)D4semidirect
153. C2×Q16×C31D4semidirect
162. C2×SD16×C31D4semidirect
368. #23894C31direct (N × H)
467. #3586C2×C31semidirect
468. #3585C2×C31semidirect
469. #3020C2×C31semidirect
470. #3019C2×C31semidirect
471. #3010C2×C31semidirect
472. #3009C2×C31semidirect
473. #2019C2×C31semidirect
474. #2017C2×C31semidirect
475. #2009C2×C31semidirect
476. #2008C2×C31semidirect
477. #1903C2×C31semidirect
478. #1902C2×C31semidirect
479. #1881C2×C31semidirect
480. #1881C2×C31semidirect
481. #1794C2×C31semidirect
515. C2×2−1+4C22×C31semidirect
530. #575C22×C31semidirect
531. #575C22×C31semidirect
534. C2×#137C22×C31semidirect
538. C22×SD16C22×C31semidirect
540. #568C22×C31semidirect
541. #536C22×C31semidirect
542. #535C22×C31semidirect
552. #421C22×C31semidirect
553. #421C22×C31semidirect
554. #421C22×C31semidirect
555. #419C22×C31semidirect
556. #418C22×C31semidirect
558. #416C22×C31semidirect
559. C2×#101C22×C31semidirect
560. C2×#100C22×C31semidirect
561. #410C22×C31semidirect
562. #408C22×C31semidirect
563. #408C22×C31semidirect
564. #408C22×C31semidirect
565. #344C22×C31semidirect
566. #344C22×C31semidirect
567. #341C22×C31semidirect
568. #338C22×C31semidirect
585. 2−1+4D4×C31semidirect
593. H(5,𝔽2)D4×C31semidirect
631. #137D4×C31semidirect
649. AGL(1,ℤ/8)D4×C31semidirect
661. C2×Q16D4×C31semidirect
670. C2×SD16D4×C31semidirect
712. C31#23894direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C31×#35862
C31×#35852
C31×#30202
C31×#30192
C31×#30102
C31×#30092
C31×#20192
C31×#20172
C31×#20092
C31×#20082
C31×#19032
C31×#19022
C31×#18812
C31×#17942
#2389431